Simulation Modelling Practice and Theory 18 (2010) 836–849

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Simulation Modelling Practice and Theory

journal homepage: www.elsevier .com/locate /s impat

Surge arresters’ circuit models review and their applicationto a Hellenic 150 kV transmission line

C.A. Christodoulou a, L. Ekonomou b,*, A.D. Mitropoulou a, V. Vita b, I.A. Stathopulos a

a National Technical University of Athens, School of Electrical and Computer Engineering, High Voltage Laboratory, 9 Iroon Politechniou St.,Zografou Campus, 157 80 Athens, Greeceb A.S.PE.T.E. – School of Pedagogical and Technological Education, Department of Electrical Engineering Educators, N. Yeraklion, 141 21 Athens, Greece

a r t i c l e i n f o

Article history:Received 31 July 2009Received in revised form 27 January 2010Accepted 28 January 2010Available online 4 February 2010

Keywords:Surge arrestersSimulationTransmission linesFailure probabilityModels

1569-190X/$ - see front matter � 2010 Elsevier B.Vdoi:10.1016/j.simpat.2010.01.019

* Corresponding author. Tel.: +30 6972702218.E-mail address: leekonom@gmail.com (L. Ekonom

a b s t r a c t

Metal oxide surge arresters are used to protect medium and high voltage systems andequipment against lightning and switching overvoltages. Measurements of the residualvoltage of the metal oxide surge arresters indicate dynamic characteristics with the resid-ual voltage to increase as the current front time descends and the residual voltage to reachits maximum, before the arrester current reaches its peak. Thus, the metal oxide surgearresters cannot be modeled by only a non-linear resistance, since its response dependson the magnitude and the rate of rise of the surge pulse. Several frequent dependent mod-els have been proposed, in order to simulate this dynamic frequency-dependent behavior.This study constitutes a review of the most important models, which are tested usingPSCAD. The residual voltage of each model, implying 5 kA, 10 kA and 20 kA 8/20 ls impulsecurrent, is compared with the manufacturers’ datasheet. The models are also used to studythe lightning performance of a Hellenic 150 kV transmission line with the arresters imple-mented on every one, two or three towers, calculating their failure probability. The resultsshow that all models function with a satisfactory accuracy and the differences among themodels arise in the difficulties of the parameters’ estimation.

� 2010 Elsevier B.V. All rights reserved.

1. Introduction

The distribution and transmission lines and their electrical equipment are exposed to many stresses, caused by atmosphericdischarges and switching overvoltages, resulting interruption of the normal operation of the electrical network and damage ofthe equipment. The most common method, in order to improve the lightning performance and reduce the number of faults inhigh voltage transmission lines, is the installation of overhead ground wires, which intercept lightning strokes, that otherwisewill terminate on the phase conductors. Ground wires offer effective protection, when low values of ground resistance areachieved. When lightning strikes the tower structure or overhead shield wire, the lightning discharge current, flowing throughthe tower and tower footing resistance, produces potential differences across the line insulation. If the line insulation strengthis exceeded, flashover occurs, i.e. a backflashover. Since the tower voltage is highly dependent on the tower resistance, conse-quently footing resistance is an extremely important factor in determining lightning performance [1,2].

Apart from the ground wires, the installation of surge arresters is considered the most effective protection against thesetransient overvoltages, especially for areas with high ground resistances and keraunic level. The arresters are installedbetween phase and earth and act as bypath for the overvoltage impulse. They are designed to be insulators for nominaloperating voltage, conducting at most few milliamperes of current and good conductors, when the voltage of the line exceeds

. All rights reserved.

ou).

C.A. Christodoulou et al. / Simulation Modelling Practice and Theory 18 (2010) 836–849 837

design specifications to pass the energy of the lightning strike to the ground. Several different types of arresters are available(e.g. gapped silicon carbide, gapped or non-gapped metal oxide) and all perform in a similar manner: they function as highimpedances at normal operating voltages and become low impedances during surge conditions. The conventional silicon car-bide arresters with gaps have been replaced in the last years by gapless metal oxide arresters, providing significant advan-tages, namely:

� superior protective characteristics,� higher reliability,� better performance under polluted environment,� ability to withstand higher temporary overvoltages and� multiple voltages surges for longer periods of time.

In comparison to arresters with gaps, metal oxide arresters reliably limit the voltage to low values, due to the high non-linearity of the V–I characteristic, even for steep impulses, with very fast response time [3–5]. The main characteristics of asurge arrester are [5]: maximum continuous operating voltage (MCOV), which must be greater than the maximum networkoperating voltage with a safety margin of 5%, rated voltage, which must be 1.25 �MCOV, protection level and capacity towithstand the energy of transient overvoltages.

The adequate circuit representation of metal oxide surge arresters plays an important role in the insulation coordinationstudies of power systems. The estimation of the arresters failure probability contributes to a more optimum design of a newline or the improvement of an already existing one, intending to a more effective lightning protection, reducing the opera-tional costs and providing continuity of service. Surge arresters improve the lightning performance of the line, but there isalso the possibility of damage of the arresters, due to high currents impulses that pass through them. The reduction of thelightning failures of the line after arresters’ installation and the failure rate of the arresters, when they absorb energy higherthan their absorption capability, are dependent on tower footing resistance, arresters’ electrical characteristics, arresters’installation interval, the lightning current waveform and the keraunic level of area [6–11]. The theoretical computation ofsurge arresters failure probability is also dependent on the selected model for the simulation process. The circuit represen-tation of metal oxide surge arresters is a significant issue, since metal oxide surge arresters present dynamic behavior,mainly dependent on the time to crest of the injected impulse current, i.e. residual voltage reaches its peak before the peakof the impulse current and becomes higher for lower front times of the injected impulse [12].

In this study a review of the most important metal oxide surge arresters is performed. According to the literature variousmodels have been proposed, in order to reproduce the frequency-dependent behavior of metal oxide surge arresters. Themost widely used and popular ones are the IEEE model [12], the Pinceti–Gianettoni model [13] and the Fernandez–Diazmodel [14]. The last two models are simpler versions of the IEEE model. The arresters models are simulated and comparedusing an appropriate computer program (PSCAD) presenting and analyzing the effect of each model in the arresters’ failureprobability calculation.

2. Metal oxide arresters circuit models

Metal oxide arresters present a highly non-linear voltage–current characteristic (Fig. 1), according to the equation[15,16]:

Fig. 1. Metal oxide surge arrester’s voltage–current characteristic [4].

838 C.A. Christodoulou et al. / Simulation Modelling Practice and Theory 18 (2010) 836–849

I ¼ kVa; a > 1 ð1Þ

where

I is the current through the arrester,V is the voltage across the arrester,a is a non-linearity exponent (measure of non-linearity) andk is a constant depended on the arresters type.

The value a characterizes the non-linear V–I characteristic; the greater the value of a, the ‘‘better” the varistor. Modernarresters have values of a between 25 and 60.

V–I characteristic must be determined using measurements performed with brief pulse currents, such as an 8/20 lswaveshape, in order to avoid effects such as varistor heating. Furthermore, the interval between the consecutive surges inthe laboratory must be sufficiently long to allow varistor revert room temperature prior to the application of the consequentsurge [17]. Data and measurements on characteristics of metal oxide surge arresters indicate a dynamic behavior. The resid-ual voltage of the arrester depends on the current surge waveform shape and increases as the current front time decreases[12,16,17]. This increase of the residual voltage could reach approximately 6% when the front time of the discharge current isreduced from 8 ls to 1.3 ls [12,18,19].

Based on the above, it can be concluded that metal oxide surge arresters cannot be modeled by only a non-linear resis-tance, since their response depends on the magnitude and the rate of rise of the surge pulse. Metal oxide arresters behavedifferently for various surge waveforms, depending each time on the peak and the slope of the overvoltage. Several frequentdependent models have been proposed, in a way that the model simulation results correspond to the actual behavior of thearrester. The existing models [2,6–10] differ in the parameters’ estimation procedure, but all are efficient enough to simulatethe frequency-depended behavior of the arresters.

2.1. The physical model

The basic varistor model is a general non-frequency-dependent model for metal oxide protective devices, presented inFig. 2. L is the inductance of conducting leads and C is the capacitance of the device package and zinc oxide material. Accord-ing to the conduction mechanism of the varistor microstructure, the resistive component of the voltage–current character-istic can be divided into three regions: low, medium and the high-current region. At low currents, the varistor can be treatedas a high value resistance RL, and at very high currents the low value bulk resistance RB of the zinc oxide grains dominates thevaristor response [13,16,20,21].

2.2. The IEEE model

The IEEE Working Group 3.4.11 [12] proposed the model of Fig. 3, including the non-linear resistances A0 and A1, sepa-rated by a R–L filter. For slow front surges the filter impedance is low and the non-linear resistances are in parallel. For fastfront surges filter impedance becomes high, and the current flows through the non-linear resistance A0.

The inductance L1 and the resistance R1 comprise the filter between the two varistors, since the inductance L0 is associ-ated with magnetic fields in the vicinity of the arrester. R0 stabilizes the numerical integration and C represents the terminal-to-terminal capacitance. The equations for the above parameters and the per-unit V–I characteristic of the varistors are givenin [12]:

AoC RL

L

RB

Fig. 2. The physical model.

Lo L1

A1AoC

Ro R1

Fig. 3. The IEEE model [12].

C.A. Christodoulou et al. / Simulation Modelling Practice and Theory 18 (2010) 836–849 839

L1 ¼ ð15dÞ=n lH ð2ÞR1 ¼ ð65dÞ=n X ð3ÞL0 ¼ ð0:2dÞ=n lH ð4ÞR0 ¼ ð100dÞ=n X ð5ÞC ¼ ð100nÞ=d pF ð6Þ

where

d is the length of arrester column in meters andn is the number of parallel columns of metal oxide disks.

2.3. The Pinceti–Gianettoni model

This model is based on the IEEE model with some differences. There is no capacitance and the resistances R0 and R1 arereplaced by one resistance (approximately 1 MX) at the input terminals, as shown in Fig. 4. The non-linear resistors arebased on the curves of [12]. The inductances L0 and L1 are calculated using the equations [13]:

L0 ¼14� Vrð1=T2Þ � Vrð8=20Þ

Vrð8=20Þ� Vn lH ð7Þ

L1 ¼1

12� Vrð1=T2Þ � Vrð8=20Þ

Vrð8=20Þ� Vn lH ð8Þ

where

Vn is the arrester’s rated voltage,Vr8/20) is the residual voltage for a 8/20 10 kA lightning current andVr1/T2) is the residual voltage for a 1/T2 10 kA lightning current.

The advantage of this model in comparison to the IEEE model is that there is no need for knowing the arresters’ physicalcharacteristics, but there is only a need for the knowledge of the electrical data, given by the manufacturer.

2.4. The Fernandez–Diaz model

Based also on IEEE model, A0 and A1 are separated by L1, while L0 is neglected (Fig. 5). C is added in arrester terminals andrepresents terminal-to-terminal capacitance of the arrester.

This model does not require iterative calculations since the required data are obtained from the manufacturer’s datasheet.The procedure for the computation of the parameters is given in [10]. The V–I characteristics for A0 and A 1 are calculatedusing manufacturers’ data, considering the ratio I0 to I1 equal to 0.02. The inductance L1 is given as:

A1AoR

L1Lo

Fig. 4. The Pianceti–Gianettoni model [13].

A1AoR

L1

C

Fig. 5. The Fernandez–Diaz model [14].

Table 1Electric

MCORateMax

HeigInsuCreeEner

Table 2Parame

LRL

RB

C

Table 3Parame

L1

R1

L0

R0

C

840 C.A. Christodoulou et al. / Simulation Modelling Practice and Theory 18 (2010) 836–849

L1 ¼ nL01 ð9Þ

where

n is a scale factor andL01 is given in [14], computing the percentage increase of the residual voltage as:

DVres ð%Þ ¼Vrð1=T2Þ � Vrð8=20Þ

Vrð8=20Þ� 100 ð10Þ

where

Vr(8/20) is the residual voltage for a 8/20 lightning current and,Vr(1/T2) is the residual voltage for a 1/T2 lightning current with the nominal amplitude.

3. Simulation results

The simulations for each one model were performed using PSCAD program for a one-column 150 kV MO arrester, withheight 952 mm. In Table 1 the electrical and insulation characteristic data of the used surge arrester are given. This typeof surge arrester is mainly used in the Hellenic transmission system.

al and insulation data of the used in the simulations surge arrester.

V 96 kVd voltage 120 kVimum residual voltage with lightning current 8/20 ls 5 kA 289 kV

10 kA 312 kV20 kA 354 kV

ht 3930 mmlation material Silicon rubberpage 1428 mmgy withstand 1440 kJ

ters for the physical model.

1.52 lY1 MX0.04 X107 pF

ters for the IEEE model.

14.28 lY64.88 X0.19 lY95.2 X105.4 pF

Table 4Parameters for the Pinceti–Gianettoni model.

L1 2.076 lYL0 0.69 lYR 1 MX

Table 5Parameters for the Fernandez–Diaz model.

L1 1.07 lYC 105.4 pFR 1 MX

0.00 0.01m 0.02m 0.03m

0

50

100

150

200

250

300

kV

Vrfern Vrpinc VrIEEE Vrphys

0.0

2.0

4.0

6.0

kA

Impulse Current(kA)

Fig. 6. Residual voltage for a 5 kA current impulse (8/20 ls).

C.A. Christodoulou et al. / Simulation Modelling Practice and Theory 18 (2010) 836–849 841

In Tables 2–5 the computed parameters for each one model are shown, according to the procedures described in Section2.

The residual voltage waveforms of each model for three impulse currents 8/20 ls (5 kA, 10 kA, 20 kA) are shown in Figs.6–8.

The simulation results for each model are compared with the manufacturer’s data (Table 6). The relative error is com-puted using the equation:

e ¼ Vrsimulation � Vrmanufacturer

Vrmanufacturer� 100% ð11Þ

where

Vrsimulation is the residual voltage from the simulation andVrmanufacturer is the residual voltage given by the manufacturer datasheet.

Fig. 9 compares the relative errors (in relation to manufacturer’s recorded residual voltage) of the four models at everydischarge current level. The physical model and the Pinceti–Gianettoni model seem to underestimate the residual voltage

0.00 0.01m 0.02m 0.03m

0

50

100

150

200

250

300

(kV

)

Vrfern Vphys VrIEEE Vrpinc

0.0

2.0

4.0

6.0

8.0

10.0

12.0

(kA

)

Impulse Current (kA)

Fig. 7. Residual voltage for a 10 kA current impulse (8/20 ls).

0.00 0.01m 0.02m 0.03m

0

50

100

150

200

250

300

350

(kV

)

Vrfern VrIEEE Vrphys Vrpinc

0.0

5.0

10.0

15.0

20.0

25.0

(kA

)

Impulse Current(kA)

Fig. 8. Residual voltage for a 20 kA current impulse (8/20 ls).

842 C.A. Christodoulou et al. / Simulation Modelling Practice and Theory 18 (2010) 836–849

(negative error), in contrast to the other two dynamic models that predict higher residual voltage. It can be observed that theIEEE model presents the lower error, offering higher accuracy, mainly due to its complexity in comparison to the othermodels.

Table 6Residual voltages and relative errors for each model.

I (kA) Residual voltage (kV)

Manufacturers’datasheet

Physicalmodel

e (%) IEEEmodel

e (%) Pinceti–Gianettonimodel

e (%) Fernandez–Diazmodel

e (%)

5 289 281.94 �2.44 292.96 1.37 282.61 �2.21 293.73 1.6310 312 304.17 �2.51 316.46 1.43 305.51 �2.08 317.36 1.7220 354 345.22 �2.48 358.92 1.39 346.42 �2.14 359.91 1.67

C.A. Christodoulou et al. / Simulation Modelling Practice and Theory 18 (2010) 836–849 843

The obtained simulation waveform must be as close as possible to the recorded measurements. Therefore, besides thepeak residual voltage, the absorbed energy by the arrester must be also checked. This constitutes a very important factorin order to compute the arresters’ failure probability. The lightning energy absorbed by an arrester is given by the equation:

E ¼Z t

to

VðtÞ � IðtÞdt ð12Þ

where

V(t) is the residual voltage of the arrester in kV andI(t) is the value of the discharge current through the arrester in kA.

It must be mentioned that when the arrester energy absorption exceeds their withstand capability, the arrester isdamaged.

Laboratory measurements obtained from [22] are used in order to show the relationship between the arrester’s modelselection and the energy absorption. In [22] the absorbed energy of a 7.5 kV surge arrester has been measured and it hasbeen compared with ATP results for the IEEE and the Pinceti–Gianettoni model. In the current study the physical, the IEEE,the Pinceti–Gianettoni and the Fernandez–Diaz models are simulated using PSCAD, following the same procedure that hasbeen used for the 150 kV arrester (Figs. 6–8, Table 6). Table 7 shows the recorded [22] and the calculated absorbed by thearrester energy for each of the examined model.

The small difference between the computed results and those presented in [22] are a consequence of the different com-puter simulation tools used (ATP vs PSCAD). All the simulated models are able to reproduce with good accuracy the residualvoltage and the absorbed energy. Although the Fernandez–Diaz model gives in general greater peak residual voltage values,the IEEE model absorbs more energy; this is owned to the shape of the waveform, since the area under the residual voltagecurve is bigger for the IEEE model. The advantage of the three dynamic models, apart from the fact that they decrease therelative error, is that they can represent the frequency-dependent behavior of the metal oxide surge arrester, which is reallyimportant when the time to crest value of the lightning current is not constant.

5 10 20-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Discharge current (kA)

Rel

ativ

e er

ror

(%)

physical

IEEEPinceti

Fernandez

Fig. 9. Relative errors of the residual voltage for each model.

Table 7Absorbed energy for each examined model.

Measurement Physical model e (%) IEEE model e (%) Pinceti–Gianettoni Model e (%) Fernandez–Diaz model e (%)

6413.1 J 6269.4 J �2.24 6501.7 J 1.38 6487.3 J 1.15 6499.2 J 1.34

844 C.A. Christodoulou et al. / Simulation Modelling Practice and Theory 18 (2010) 836–849

4. Evaluation of arresters failure probability using the equivalent circuit models

The use of the proposed arrester circuit models for lightning performance studies offers more reliable and accurate re-sults, in comparison to the simple non-linear resistance model that the various program tools include in their libraries, sincethese dynamic frequency-dependent models represent more efficiently the residual voltage waveform. The four models, pre-sented in Section 2, are implemented, using an appropriate computer program, in Hellenic high voltage transmission lines.Arresters’ failure probability is computing with the use of each model, taking into consideration parameters such as theinstallation interval and the tower footing resistance. In more detail, the arrester’s failure probability depends on:

a. their energy absorption capability, which is the maximum level of energy injected into the arrester, at which it canstill cool back down to its normal operating temperature.

b. the installation interval, the distance in which surge arresters are installed. In regions with high keraunic level andgrounding resistance a more dense arresters installation is required.

c. the tower footing resistance, for direct strikes to phase conductors, low tower footing resistance results in higher en-ergy through the arrester; for strikes on towers or on ground wires, high resistances increase the arresters failure probability.

d. the electrogeometrical model: when the downward leader approaches to earth, the point that the leader will hit de-pends on the magnitude of the lightning stroke current. The electrogeometrical model represents this idea by using the strik-ing distance concept, for the ground wire or the ground. Considering rc,g = aIb, is designed the model of Fig. 10 [23].

The probabilities hA(IP) and hB(IP) that the lightning strikes a phase conductor or the overhead ground correspondingly,can be estimated for each value of the peak current IP using Eqs. (13) and (14):

hAðIpÞ ¼XC

Xð13Þ

hBðIpÞ ¼X � XC

Xð14Þ

rc

rc

rg

XXc

groundwire

phase

Fig. 10. Electrogeometrical model: representation of ground wires and phase conductors [23].

u1 u2u1'

u1'’

Fig. 11. Shielding failure on a transmission line.

u1u2

u3

Fig. 12. Backflashover failure on a transmission line.

C.A. Christodoulou et al. / Simulation Modelling Practice and Theory 18 (2010) 836–849 845

846 C.A. Christodoulou et al. / Simulation Modelling Practice and Theory 18 (2010) 836–849

All the above factors are summarized in the following equation [6–11]:

P ¼Z 1

Tr

Z 1

IAðTtÞf ðIpÞ � hAðIPÞdIP

( )gðTtÞdTt þ

Z 1

Tt

Z 1

IBðTtÞf ðIPÞ � hBðIPÞdIP

( )gðTtÞdTt ð15Þ

where: P is the total failure probability of an arrester, IA(Tt) is the minimum stroke peak current in kA required to damage thearrester, when lightning hits on a phase conductor, depending on each time-to-half value, IB(Tt) is the minimum stroke peakcurrent in kA required to damage the arrester, when lightning hits on the overhead ground wire, depending on each time-to-half value, f(IP) is the probability density function of the lightning current peak value, g(Tt) is the probability density functionof the time-to-half value of the lightning current and Tr is the rise time of the incident waveform,

Figs. 11 and 12 show lightning strokes on the phase conductor or on ground wire, correspondingly, for a high voltagetransmission line. When lightning hits the tower or the ground wire, an increase on the potential of the metal structureof the tower is caused (depending on the grounding resistance) up to the critical flashover voltage that leads to a backflas-hover. The possibility of a shielding failure, i.e. a failure due to a lightning hit on the phase conductor, is small, since lightningcurrents that strike the protected conductors are not high enough, according to the electrogeometrical model.

Surge arresters are installed between the phase conductors and earth, in order to prevent the flashovers along the insu-lators. In case of direct stroke on phase conductors, the surge arrester becomes conductive, leading the overvoltage current tothe ground. When lightning strikes the tower or the ground wires (Fig. 13), one part travels in both directions of the groundwire (u1 and u2), one part goes down to the grounding system (u3), and one part flows through the arrester, which conductsbackwards, to the line, splitting also to both directions (u4 and u5). The sharing of the lightning current depends mainly onthe tower footing resistance. The voltage wave travelling along the phase conductor may cause flashover to the next towerhence the installation of surge arresters with a dense step is necessary, especially in regions with high keraunic level andhigh grounding impedances, in order to divert the remaining overvoltage wave to the ground (u6). This will continuouslyoccur from one tower to another (u7), until all the lightning current is diverted to earth.

The waveform of the lightning surge has been produced by a double exponential wave, considering the time to crest valueconstant at 2 ls. The peak current and time-to-half distribution functions used, are those performed by Berger in Monte SanSalvatore [11]. The surge impedance values are 400 X for phases and 700 X for ground wires. The towers are represented asdistributed parameters lines 200 X. In the simulation, surge arresters are installed on all phases and three cases are tested. In

u1u2

u4

u3

u5u7

u6

u8

u9

u10

Fig. 13. Arresters conduction for a lightning stroke on the tower.

Table 8Arresters failure probability for each one case and each one model.

TFR P1 (%) P2 (%) P3 (%) P1 (%) P2 (%) P3 (%)

Physical model IEEE20 X 0.144 0.306 0.464 0.183 0.378 0.58840 X 0.216 0.374 0.539 0.267 0.447 0.62760 X 0.287 0.425 0.584 0.357 0.521 0.66380 X 0.403 0.536 0.705 0.478 0.629 0.841120 X 0.714 0.751 0.827 0.851 0.902 0.935

Pincetti–Gianettoni Fernandez–Diaz20 X 0.167 0.344 0.522 0.178 0.352 0.57940 X 0.238 0.402 0.589 0.252 0.425 0.61260 X 0.330 0.478 0.625 0.349 0.492 0.64280 X 0.439 0.596 0.792 0.465 0.607 0.814120 X 0.776 0.843 0.900 0.792 0.895 0.916

C.A. Christodoulou et al. / Simulation Modelling Practice and Theory 18 (2010) 836–849 847

Case 1 arresters are installed on every tower, in Case 2 arresters are installed on every second tower and in Case 3 arrestersare installed on every third tower.

The waveforms of the arresters’ terminal voltage and the current flowing through them are used in order to calculate theenergy dissipated by the arresters. The arresters failure probability is computed using (15). In order to find the minimumstroke currents for each time-to-half value IA(Tt) and IB(Tt), required for the arresters’ failure, an arithmetic method pro-grammed in Matlab is used, properly combined with PSCAD simulation procedures. Considering a stroke on phase or onground wires, for each time-to-half value the lighting current that damages the arresters is calculated, with a time-to-halfrange from 10 ls to 1000 ls and step 1 ls.

In Table 8 the results for various tower footing resistance values are given. The failure probability increases as groundingresistance increases, in the same way for all the models. An arrester’s failure can be caused by a lightning strike to a phaseconductor, to the tower or to the overhead ground wire. For direct strikes to phase conductors, low tower footing resistanceresults in higher energy through the arrester; for strikes on towers or on ground wires, high resistances increase the arrestersfailure probability. The probability of failure due to strike on phases is small, so strike on ground wire is the dominant casefor the determination of the arresters’ failure rate.

Fig. 14 shows the arresters failure probability in relation to the tower footing resistance, for the IEEE model, for the threeanalyzed case studies. It can be observed that smaller arrester installation interval decreases the arresters failure rate. There-fore for regions with high tower footing resistance, arresters installation on every tower is recommended.

Fig. 15 presents the arrester failure probability in relation to the tower footing resistance for all models, when the arrest-ers are installed on every tower (Case 1). Although the Fernandez–Diaz model gives greater peak value of the residual volt-age, the IEEE model gives a little greater probability, mainly due to the fact that the area under the voltage curve is bigger, so

20 30 40 50 60 70 80 90 100 110 1200.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Grounding resistance (Ohm)

Arr

este

rs' F

ailu

re P

roba

bilit

y

Case 1

Case 2

Case 3

Fig. 14. Arrester’s failure probability versus tower footing resistance for the IEEE model and for each one of the three analyzed case studies.

20 30 40 50 60 70 80 90 100 110 1200.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Grounding resistance (Ohm)

Arr

este

rs'F

ailu

re P

roba

bilit

y (%

)

physical

IEEEPinceti

Fernandez

Fig. 15. Arresters failure probability versus tower footing resistance for all models and for arresters installed on every tower.

848 C.A. Christodoulou et al. / Simulation Modelling Practice and Theory 18 (2010) 836–849

the absorbed energy will be greater. As expected, the physical model gives the lowest failure probability, since computeslower residual voltage (Table 6) and absorbed energy (Table 7). The comparison with field inspection data for the annualfailure rate of the arresters installed on a line will be useful for the study of the models’ accuracy. However, the computedresults show that all models are appropriate for lightning performance simulation and failure probability estimation. Thusthe selection of the most suitable model for a study depends on the available data.

5. Conclusions

This study presents a review of the most used frequency-depended models for metal oxide surge arresters. The residualvoltage and the absorbed energy for each model applying impulse currents were computed using PSCAD, and the simulationpredictions were compared with real measured data. All models represent successfully the arresters’ lightning behavior, pre-senting an acceptable error. However, the physical model is the only one that cannot represent the dependence of the resid-ual voltage peak with the time to crest value. Therefore the use of the dynamic models, which reproduce more efficiently thereal behavior of the metal oxide surge arresters, is suggested. Furthermore the computation of the energy injected to thearrester is a very important issue, since it is an indicator of the curve-fitting of the simulated and the measured waveformand affects the estimation of the arrester’s failure probability. Finally, the models were also used in order to estimate thearrester’s failure probability of a 150 kV Hellenic transmission line. The analysis showed that the three frequency-dependentmodels have an efficient dynamic behavior and can be used to estimate the lightning performance of high voltage transmis-sion lines. Finally it has been proved that the decision on which model should be used depends on the available data, thecomplexity of the system and the demanded speed of the simulation, since the Pinceti–Gianetoni and the Fernandez–Diazmodel are simpler than the IEEE model.

References

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